In the field of optical CT or the like in a broad sense, including interior measurement, there are conventionally known measuring methods of gaining information about the interior of the measured object, using the weight function or contribution function, and a number of reports have already been made about the weight functions and others applied thereto. These are described, for example, in the following documents.
(1) S. Arridge: SPIE Institutes for Advanced Optical Technologies, Vol. IS11, Medical Optical Tomography: Functional Imaging and Monitoring, 35-64(1993); (2) R. L. Barbour and H. L. Graber: ibid. 87-120(1993); (3) H. L. Graber, J. Chang, R. Aronson and R. L. Barbour: ibid. 121-143(1993); (4) J. C. Schotland, J. C. Haselgrove and J. S. Leigh: Applied Optics, 32, 448-5453(1993); (5) Chang, R. Aronson, H. L. Graber and R. L. Barbour: Proc. SPIE, 2389, 448-464(1995); (6) B. W. Pogue, M. S. Patterson, H. Jiang and K. D. Paulsen: Phys. Med. Biol. 40, 1709-1729(1995); (7) S. R. Arridge: Applied Optics, 34, 7395-7409(1995); (8) H. L. Graber, J. Chang, and R. L. Barbour: Proc. SPIE, 2570, 219-234(1995); (9) A. Maki and H. Koizumi: OSA TOPS, Vol. 2, 299-304(1996); (10) H. Jiang, K. D. Paulsen and Ulf L. Osterberg: J. Opt. Soc. Am. A13, 253-266(1996); (11) S. R. Arridge and J. C. Hebden: Phys. Med. Biol. 42, 841-853(1997); (12) S. B. Colak, D. G. Papaioannou, G. W. 't Hooft, M. B. van der Mark, H. Schomberg, J. C. J. Paasschens, J. B. M. Melissen and N. A. A. J. van Astten: Applied Optics, 36, 180-213(1997).
However, the interior information measuring methods of optical CTs and others disclosed in the above documents (1) to (12) and the weight functions applied thereto included the problems discussed below and thus posed significant problems in measurement accuracy and applicability. In fact, no report has been made yet about an example of practical use of optical CT with satisfactory performance in the foregoing field.
Specifically, the first problem in the conventional optical CT and others is that the photon migration analysis or photon migration model in the medium is based on the photon diffusion equation as application of diffusion approximation to the transport equation. In other words, since the diffusion approximation holds only in media sufficiently larger than the mean free pathlength of photons in the medium, there is a problem that it is impossible to handle relatively small media, tissue of complicated interior shape, and media of complicated shape. In addition, the diffusion approximation is premised on isotropic scattering, and thus application thereof to the measurement of the measured object like living tissue having anisotropic scattering characteristics will pose a problem that there occur considerable errors due to the approximation of anisotropic scattering to isotropic scattering.
Further, differential equations such as the diffusion equation and the like involve a bothersome problem that even with any numerical computation approach such as the analytical or finite element method, boundary conditions (the shape of the medium, reflection characteristics at interfaces, etc.) must be preliminarily set and then a solution can be determined. Namely, in the case of the measured object like living tissue, the boundary conditions normally vary depending upon a place to be measured, the wavelength of light used in measurement, and so on, and for improvement in accuracy on the basis of correction for influence of these factors, it is necessary to repeat complicated calculations at every change of the boundary conditions, which results in a big problem of extremely long calculation time.
The second problem is that the weight function in a narrow sense (also called the contribution function), i.e., a mean path length (weighted mean) for an ensemble of photons constituting an impulse response of the medium, or a phase delay equivalent thereto (measured in the frequency domain) is applied to the calculation of the information on the interior of the measured object. In this case, the weight function in a narrow sense (the mean path length or the phase delay equivalent thereto) varies depending upon absorption coefficients and absorption distribution, and thus handling thereof is extremely complicated. Since practical use of a calculation method taking account of such dependence inevitably requires calculations in a large iteration number, there will arise a problem that the calculation time becomes extremely long over a practical range. Therefore, the dependence on the absorption coefficients and absorption distribution is normally ignored, but this approximation can be the cause of a serious issue of increase in errors.
In order to reduce the errors due to the dependence of the weight function on the absorption coefficients and absorption distribution as described above, there is a method of calculating and applying the weight function with some appropriate absorption. However, this poses a problem that the time necessary for the calculation of the weight function with absorption is extremely longer than the time necessary for the calculation of the weight function without absorption.
For the reason described above, it is concluded that the conventional measuring methods using the weight function in a narrow sense (the mean path length or the phase delay equivalent thereto) are not practical.
Besides the application of the above weight function in a narrow sense, there is a further measuring method of applying the perturbation theory to the approximate equation of the transport equation or to the photon diffusion equation to gain the information about the interior of the measured object with the use of the relationship between signal light and optical characteristics of the scattering medium. However, this method requires extremely complex handling of the nonlinear effects (second and higher order terms). In this respect, the calculation including the second and higher order terms can be theoretically performed by a computer, but the calculation time will be huge even with the use of the currently fastest computer, so as to make practical use thereof impossible. It is thus common practice to ignore the second and higher order terms. For this reason, this method had a problem that there arose large errors due to interaction between absorbing regions in reconstruction of an optical CT image of a medium containing a plurality of relatively strong absorbing regions.
As described above, the measuring methods of gaining the information about the interior of the measured object, such as the conventional optical CT and the like, failed to obtain a reconstructed image with satisfactory accuracy and had the significant issues as to the spatial resolution, image distortion, quantitation, measurement sensitivity, required measurement time, and so on, which made practical use thereof difficult.
The Inventor contemplated that the following was important in order to break through the above circumstances, and has pursued a series of studies. Namely, an important subject for achievement of a measuring method capable of obtaining the information about the interior of the measured object, particularly, for achievement of optical CT, is to clarify the details of behavior of photons migrating in living tissue as a strong scattering medium, more precisely describe the relation between detected signal light and the optical characteristics of the scattering medium (scattering absorber) containing an absorptive constituent, and develop a new algorithm of reconstructing an optical CT image by making use of the signal light and the relation between the signal light and the optical characteristics of the scattering medium. Then the Inventor contemplated applying the Microscopic Beer-Lambert Law (hereinafter referred to as “MBL”) to the analysis of the behavior of photons migrating in the scattering medium and making use of information about the photon path distribution, i.e., about where photons have passed, for the reconstruction of optical CT image.
Then the Inventor has proposed a photon migration model (a finite grid model) corresponding to the scattering media, based on the MBL, derived an analytic equation representing the relation between the optical characteristics of the scattering media and the signal light, and developed methods of analyzing the behavior of photons in the scattering media. The Inventor and others reported the results of these, for example, in the following documents.
(13) Y. Tsuchiya and T. Urakami: “Photon migration model for turbid biological medium having various shapes”, Jpn. J. Appl. Phys. 34. Part 2, pp. L79-81(1995); (14) Y. Tsuchiya and T. Urakami, “Frequency domain analysis of photon migration based on the microscopic Beer-Lambert law”, Jpn. J. Appl. Phys. 35, Part 1, pp. 4848-4851(1996); (15) Y. Tsuchiya and T. Urakami: “Non-invasive spectroscopy of variously shaped turbid media like human tissue based on the microscopic Beer-Lambert law”, OSA TOPS, Biomedical Optical Spectroscopy and Diagnostics 1996, 3, pp. 98-100(1996); (16) Y. Tsuchiya and T. Urakami: “Quantitation of absorbing substances in turbid media such as human tissues based on the microscopic Beer-Lambert law”. Optics Commun. 144, pp. 269-280(1997); (17) Y. Tsuchiya and T. Urakami: “Optical quantitation of absorbers in variously shaped turbid media based on the microscopic Beer-Lambert law: A new approach to optical computerized tomography”, Advances in Optical Biopsy and Optical Mammography (Annals of the New York Academy of Sciences), 838, pp. 75-94(1998); (18) Y. Ueda, K. Ohta, M. Oda, M. Miwa, Y. Yamashita, and Y. Tsuchiya: “Average value method: A new approach to practical optical computed tomography for a turbid medium such as human tissue”, Jpn. J. Appl. Phys. 37, Part 1. 5A, pp. 2717-2723(1998); (19) Yutaka Tsuchiya; “Reconstruction of optical CT image based on Microscopic Beer-Lambert Law and average value method,” O plus E, Vol. 21, No.7, 814-821; (20) H. Zhang, M. Miwa, Y. Yamashita, and Y. Tsuchiya: “Quantitation of absorbers in turbid media using time-integrated spectroscopy based on microscopic Beer-Lambert law”, Jpn. J. Appl. Phys. 37, Part 1, pp. 2724-2727(1998); (21) H. Zhang, Y. Tsuchiya, T. Urakami, M. Miwa, and Y. Yamashita: “Time integrated spectroscopy of turbid media based on the microscopic Beer-Lambert law: Consideration of the wavelength dependence of scattering properties”, Optics Commun. 153, pp. 314-322(1998); (22) Y. Tsuchiya, H. Zhang, T. Urakami, M. Miwa, and Y. Yamashita: “Time integrated spectroscopy of turbid media such as human tissues based on the microscopic Beer-Lambert law”, Proc. JICAST'98/CPST'98, Joint international conference on Advanced science and technology, Hamamatsu, August 29-30, pp. 237-240(1998); (23) H. Zhang, T. Urakami, Y. Tsuchiya, Z. Liu, and T. Hiruma: “Time integrated spectroscopy of turbid media based on the microscopic Beer-Lambert law: Application to small-size phantoms having different boundary conditions”, J. Biomedical Optics. 4, pp. 183-190(1999); (24) Y. Tsuchiya, Y. Ueda, H. Zhang, Y. Yamashita, M. Oda, and T. Urakami: “Analytic expressions for determining the concentrations of absorber in turbid media by time-gating measurements”, OSA TOPS, Advances in Optical Imaging and Photon Migration, 21, pp. 67-72(1998); (25) H. Zhang, M. Miwa, T. Urakami, Y. Yamashita, and Y. Tsuchiya: “Simple subtraction method for determining the mean path length traveled by photons in turbid media”, Jpn. J. Appl. Phys. 37, Part 1, pp. 700-704 (1998).
This MBL is the law that “in a microscopic view in a medium having arbitrary scattering and absorption distributions, a photon migrating in a portion having the absorption coefficient of μa, is exponentially attenuated because of absorption along a migrating zigzag photon path of length l, a survival probability of the photon is given by the value exp(−μal) independent of the scattering characteristics of the medium and the boundary conditions, and the amount of attenuation due to the absorption is μal,” and is expressed, for example, by the following equation.f(l)=f0(l)exp(−μal)  (1)
Here f(l) is a detection probability density function of photons actually measured, and f0(l) a detection probability density function of photons in a state of no absorption.
This Eq (1) indicates that in the medium having arbitrary scattering and absorption distributions, absorption and scattering events are independent of each other and that the superposition principle holds as to the absorption, i.e., that, in the case of the medium with the scattering and absorption distributions being a multiple component system, the total absorbance is given by the sum of absorbances of respective components.
The Inventor and others derived equations expressing the relations between various optical responses and optical characteristics of scattering media from the MBL represented by above Eq (1) and clarified that it was possible to describe the various responses of scattering media by an attenuation term dependent upon absorption and a term independent of absorption, separated from each other. This made it feasible to quantify the absolute value of the concentration of the absorptive constituent in the scattering medium from the relation between the absorption coefficient and the extinction coefficient specific to the absorptive constituent, based on spectral measurement of the attenuation term through use of light of multiple wavelengths.
The measuring methods based on the MBL as described above have the major feature of being theoretically unsusceptible to the shape of the medium, the boundary conditions, and the scattering, and are applicable to anisotropic scattering media and small media. However, the absorption coefficient and the absorber concentration measured herein can be correctly measured for scattering media with uniform absorption, but measurement for heterogeneous media with nonuniform absorption distribution provides a mean absorption coefficient and a mean concentration (weighted mean for photon path distribution) of photon-passing portions. Accordingly, there arose the need for determining the photon path distribution, in order to realize high-accuracy optical CT.
Then the Inventor and others further expanded the methods of analyzing the behavior of photons in the scattering media on the basis of the MBL and have developed various measuring methods applicable even to the heterogeneous scattering media (heterogeneous system) with nonuniform distributions of scattering and absorption and capable of quantitatively measuring a concentration distribution of an absorptive constituent in a scattering medium without being affected by the shape of the medium, the scattering characteristics, and so on.
Specific measuring methods derived based on the MBL heretofore by the Inventor and others include, for example, the time-resolved spectroscopy (TRS) making use of the impulse response, the time-integrated spectroscopy (TIS) making use of the time integral of the impulse response, the time-resolved gating integral spectroscopy (TGS) making use of the time-gating integral of the impulse response, the phase modulation spectroscopy (PMS) in the frequency domain, the reconstruction method of optical CT image based on the average value method (AVM), and so on. These measuring methods are described in Japanese Patent Application No. 10-144300, aforementioned Document (7), and aforementioned Documents (15) to (25).
The materialization of the new measuring methods as described above drastically improved the measurement accuracy, but the reconstruction methods of optical CT image still used the conventional weight function, i.e., the mean path length or the phase delay equivalent thereto. Specifically, a small change is given to an absorption coefficient of voxel i in an imaginary medium with a uniform absorption coefficient μ84  described by the finite grid model, its optical output is calculated by making use of the Monte Carlo calculation, the numerical calculation of the Path Integral and the transport equation, the numerical calculation of the photon diffusion equation, or the like, and the weight function (or the contribution function) Wi of voxel i is determined corresponding to the difference between optical outputs before and after the change, i.e., the deviation of light intensity, optical path length, attenuation, or the like with respect to the imaginary medium having the uniform absorption coefficient μν.